A high order hybridizable discontinuous Galerkin method for incompressible miscible displacement in heterogeneous media

TL;DR

This paper introduces a high-order hybridizable discontinuous Galerkin method for simulating incompressible miscible displacement in heterogeneous porous media, offering accurate, robust solutions without slope limiters.

Contribution

It develops a novel high-order hybridizable discontinuous Galerkin approach that efficiently solves coupled nonlinear systems in porous media flow, with optimal convergence and robustness.

Findings

Method converges optimally in 2D and 3D

No slope limiters needed due to implicit treatment

Robust performance in highly heterogeneous media

Abstract

We present a new method for approximating solutions to the incompressible miscible displacement problem in porous media. At the discrete level, the coupled nonlinear system has been split into two linear systems that are solved sequentially. The method is based on a hybridizable discontinuous Galerkin method for the Darcy flow, which produces a mass--conservative flux approximation, and a hybridizable discontinuous Galerkin method for the transport equation. The resulting method is high order accurate. Due to the implicit treatment of the system of partial differential equations, we observe computationally that no slope limiters are needed. Numerical experiments are provided that show that the method converges optimally and is robust for highly heterogeneous porous media in 2D and 3D.